2D Wave Methods ?

Manipulating the lineRenderer with a Sine wave algorithm may give you the effect you're seeking. You'll probably have to tinker with the code some more, but it seems like a good start:

example.cs

     using UnityEngine;
     using System.Collections;
      
     public class example : MonoBehaviour {
         public Color c1 = Color.yellow;
         public Color c2 = Color.red;
         public int lengthOfLineRenderer = 20;
         void Start() {
             LineRenderer lineRenderer = gameObject.AddComponent<LineRenderer>();
             lineRenderer.material = new Material(Shader.Find("Particles/Additive"));
             lineRenderer.SetColors(c1, c2);
             lineRenderer.SetWidth(0.2F, 0.2F);
             lineRenderer.SetVertexCount(lengthOfLineRenderer);
         }
         void Update() {
             LineRenderer lineRenderer = GetComponent<LineRenderer>();
             int i = 0;
             while (i < lengthOfLineRenderer) {
                 Vector3 pos = new Vector3(i * 0.5F, Mathf.Sin(i + Time.time), 0);
                 lineRenderer.SetPosition(i, pos);
                 i++;
             }
         }
     }
 

http://forum.unity3d.com/threads/creating-a-sine-wave.187154/#post-1278909

http://forum.unity3d.com/threads/creating-a-plane-from-an-array-of-vector3s-2d-water.187151/